Comparison with Conventional Deformable Models

To show the effectiveness of RDMs, they were compared with conventional classification- based deformable models (CDMs) via modified active shape models. Unlike RDMs, CDMs require good initializations to work well. Once the shape model (3D mesh) is well initialized,

Table 3.3: Quantitative comparison of segmentation accuracies (DSC) obtained by the clas- sification forest (Classification) and the multitask random forest (Multitask). p-values were computed by paired t-tests. Bold numbers indicate the better performance.

DSC (%) Classification Multitask p value Prostate 85.6±4.2 86.6±4.1 <10−3 Bladder 90.9±5.2 92.1±4.7 <10−5 Rectum 86.5±5.2 88.4±4.8 <10−5 FemurL 96.1±1.4 97.0±1.5 <10−5 FemurR 96.1±1.4 97.0±1.5 <10−5

every vertex on the shape model independently deforms along its normal direction to a position with the maximal boundary response. After an one-step deformation of all vertices, the entire shape model is often smoothed or regularized by a shape space (e.g., through PCA) before the next round of deformation. These two steps alternate until convergence or reaching the maximum number of iterations.

In this experiment, a random forest classifier was used to classify every voxel in a testing image into either “organ” or “background”. The gradient on the obtained organ likelihood map was used as the boundary response to guide CDMs. After one-step deformation, mesh smoothing and remeshing were used to regularize the shape model. This step is the same as RDMs. For a fair comparison, the random forest classifier used the same types of Haar-like features and the auto-context model as those in RDMs.

Two initialization methods have been tested for CDMs.

• Box-based initialization. The regression-based anatomy detection method [Crim- inisi et al., 2013] was utilized to automatically detect the bounding box of the target organ. Based on the detected box, the mean shape was initialized on the box center and further scaled to fit the box size. After initialization, the shape model deformed in the same way as described above.

• Multi-resolution strategy. The mean shape model was initialized to the classifica- tion mass center in the coarsest resolution. Once initialized the shape model deformed on the organ likelihood map until convergence. Afterwards, the deformed shape model was used as an initialization to the next finer resolution. The deformation was hierar- chically performed until it meets the finest resolution. The multi-resolution parameters were the same with those described in section 3.5.2.

Table 3.4 shows the segmentation accuracies obtained by RDMs and CDMs with the two initialization strategies, respectively. Because CDMs rely on local search to deform, the parameter of search range is critical to segmentation. To optimize the performance of CDMs, the search range of each organ was manually searched from 10 to 35 mm with a step size of 5 mm. From the results listed in table 3.4, it can be seen that CDMs perform reasonably well for organs with rigid shapes and stable positions, such as the prostate and femoral heads, although their performance is still inferior to RDMs’. However, they fail notably when segmenting organs with highly variable shapes, such as the bladder and rectum.

Table 3.4: Quantitative comparison (DSC) between classification-based and regression-based deformable models. Bold numbers indicate the best performance.

DSC (%) Classification Regression Box Multi-resolution Prostate 83.7±12.3 83.3±12.0 86.6±4.1 Bladder 73.1±32.4 87.1±20.0 92.1±4.7 Rectum 53.9±26.9 57.3±33.6 88.4±4.8 FemurL 95.6±4.6 95.9±7.8 97.0±1.5 FemurR 95.6±4.1 96.4±5.6 97.0±1.5

The main reason for those failures is that initialization is demanded by conventional deformable models. However, a good initialization is often difficult to obtain for flexible organs such as the bladder and rectum. Fig. 3.14 presents several typical bounding-box-

based initializations for illustration. It can be seen that it is challenging to accurately detect the bounding box of the bladder due to dramatic changes of bladder sizes and positions across subjects. For the rectum initialization, it is even more challenging. As shown in the right panel of fig. 3.14, although the detected bounding boxes (green) are reasonably good, the initialized shapes (green) are still far from the true organ boundaries (red) because of the dissimilarity between the mean rectum shape and individual rectum shapes. The highly variable shapes make the bounding-box based initialization less effective in initializing the rectum compared to other organs, such as the prostate and femoral heads that have relatively stable shapes. The same challenges also apply to the multi-resolution initialization strategy.

Figure 3.14: Typical cases of bounding-box-based initialization (Left: bladder; Right: rec- tum). The second row shows the initialized shapes according to the detected bounding boxes in the first row. The red and green contours indicate the ground-truth and the results obtained by anatomy detection, respectively.

Besides the initialization, conventional deformable models (e.g., ASM) still faces another challenge when they are applied to segmenting the rectum. That is the difficulty in deter- mining the search range. Due to the tubular structure of the rectum, large search ranges

would easily cause mesh folding as vertices of left rectum wall may find high boundary re- sponses from the right rectum wall and vice versa. On the other hand, small search ranges are insufficient to drive the deformable model onto organ boundaries if the shape model is not well initialized. These two contradictory factors make it infeasible to find a compromise search range. This also explains why the segmentation accuracy of the rectum by CDMs is much lower compared to that of other organs.

In contrast to conventional deformable models, RDMs are guided by deformation fields that provide non-local external forces to overcome the sensitivity of deformable models to initialization. Because of this fact RDMs do not require a model initialization step that is often critical in most deformable segmentation methods. This characteristic renders RDMs suitable for segmenting organs that are difficult to initialize, such as the bladder and rectum. Additionally, the deformation direction and step size of each vertex are optimally predicted during the deformation according to the underlying image appearance. This feature makes RDMs appealing to segment organs with complex shapes, such as the rectum, where the conventional deformation strategies (e.g., normal deformation direction and fixed step size) do not work. All these factors contribute to the success of RDMs in CT pelvic organ segmentation.